Exercises and problems in PhysicsNovember 2001

Experimental problem

M.228. As is well known, if we stir the
tea in a cup the submerged tea leafs gather in the middle in a small
heap (against our expectations, because we expect the particles with
higher density to drift towards the perimeter of the container). What
is the explanation of this phenomenon? Carry out some experiments to
prove the explanation. (6 points)

Theoretical problems

P.3467. Cycling without rest between two
towns the journey takes 6 hours. What is the distance between the two
towns if our average speed is 16 km/h on level surface,
12 km/h uphill and 24 km/h downhill? (3 points)

P.3468. In a heat insulated vessel there
is tap water of 15 oC. We place in it ice cubes of
-15 oC taken out of the deep-freezer. May there be no
change of state? When does only a part of the ice melt? In which case
does all of the ice melt? In which case does the water freeze? (4
points)

P.3469. The T shaped rigid body shown in
the figure consists of three uniform rods, and can rotate round
the horizontal axis t perpendicular to its plane. At the end of
the right side rod and at the point dividing it in a 2:3 ratio there
are ropes fixed and each of the ropes hold horizontal rods propped up
by wedges. The wedge holding the upper rod divides the lower rod in
3:2 ratio. The mass of the upper rod is m1, that of
the lower one is m2, and the mass of the body lying
on the upper rod is m3. What is the required mass of
the body that is to be hung on the end of the left hand side rod so as
to keep the balance. The data: m1=2.5 kg,
m2=6.0 kg, m3=7.5 kg.
(5 points)

P.3470. A carriage is joined to the end of
a slope as can be seen in the figure. A body released from the
slope from height h slides as far as the middle of the
carriage. (The friction between the body and the slope and the mass of
the wheels of the carriage are negligible.) At what height should the
body be released so that it could stop just at the end of the
carriage?
(4 points)

P.3471. We make a spiral of 0.6 m
radius and 30o slope angle of a thin but sufficiently stiff
wire and fix it in a way that its axis is vertical. Then we thread a
pierced pearl on the wire and at a given moment we let it slide
down. What speed does it gather if the friction coefficient is 0.5?
(5 points)

P.3472. We fix a block to a
spring. Hanging the spring at its end the block oscillates with a
period of 1 second. Then we put the block on a horizontal table and
hurl it towards a wall so that the spring is positioned in between as
a bumper. Colliding with the wall the spring contracts then hurls the
body back. The block stops exactly when the spring gets its neutral
size back. How much time elapsed between the spring touching the wall
and the the block stopping? (4 points)

P.3473. What are the mass percentages in a
mixture of hydrogen and helium gases where at isobar dilation 70 % of
the absorbed heat from the surrounding environment is converted to
internal energy. (4 points)

P.3474. At the endpoints of a line segment
of a length of d there are two identical positive electric
charges. What is the ratio of the electric field strength and the
electric potential in a point characterized by an angle on the
Thales' circle drawn around the line segment. (4 points)

P.3475. On a bumper at the lower end of a
vertically positioned insulator bar shown in the figure there
is a pearl of the mass m=10-4 kg and a charge
of Q1. Above at a h0=20 cm
distance there is another pearl with the same mass m and
electric charge Q2 afloat. At a given moment we kick
the lower pearl and it starts upwards at a velocity of
v0=2 m/s. How close can the lower pearl get to
the upper one at most? (The pearls can move along the bar without
friction.) (6 points)

P.3476. In a homogeneous magnetic field
there is an electron moving in a circular orbit. Can the magnetic
induction vector generated by the moving electron be greater in the
middle of the circle than the magnetic induction vector of the
homogeneous field? (5 points)

P.3477. Using thin slats we construct a
triangle shaped frame with sides a, b and c. The
overall mass of the frame is m. What is the inertial momentum
of the frame related to an axis perpendicular to the triangle and
crossing the frame in its centre of mass? (5 points)